Solve x^2=512/53

$${ x }^{ 2 } = \frac{ 512 }{ 53 }$$

Solve for x

$$x = \frac{16 \sqrt{106}}{53} \approx 3.10811476$$

$$x = -\frac{16 \sqrt{106}}{53} \approx -3.10811476$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x=\frac{16\sqrt{106}}{53} x=-\frac{16\sqrt{106}}{53}$$

Steps Using the Quadratic Formula

Subtract \frac{512}{53} from both sides.

$$x^{2}-\frac{512}{53}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{512}{53} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{512}{53}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{512}{53}\right)}}{2}$$

Multiply -4 times -\frac{512}{53}.

$$x=\frac{0±\sqrt{\frac{2048}{53}}}{2}$$

Take the square root of \frac{2048}{53}.

$$x=\frac{0±\frac{32\sqrt{106}}{53}}{2}$$

Now solve the equation x=\frac{0±\frac{32\sqrt{106}}{53}}{2} when ± is plus.

$$x=\frac{16\sqrt{106}}{53}$$

Now solve the equation x=\frac{0±\frac{32\sqrt{106}}{53}}{2} when ± is minus.

$$x=-\frac{16\sqrt{106}}{53}$$

The equation is now solved.

$$x=\frac{16\sqrt{106}}{53} x=-\frac{16\sqrt{106}}{53}$$